AIAA-2001-1182
PROGRESSIVE FAILURE STUDIES
OF COMPOSITE PANELS
WITH AND WITHOUT CUTOUTS
Damodar R. Ambur*
NASA Langley Research Center
Hampton, VA 23681-2199
Navin Jaunky^
ICASE
Hampton, VA 23681-2199
Carlos G. Davila^ and Mark Hilburger^
NASA Langley Research Center
Hampton, VA 23681-2199
Abstract
Progressive failure analyses results are pre-
sented for composite panels with and without a
cutout and are subjected to in-plane shear load-
ing and compression loading well into their post-
buckling regime. Ply damage modes such as ma-
trix cracking, fiber-matrix shear, and fiber fail-
ure are modeled by degrading the material prop-
erties. Results from finite element analyses are
compared with experimental data. Good agree-
ment between experimental data and numerical
results are observed for most structural configu-
rations when initial geometric imperfections are
appropriately modeled.
Introduction
'Head, Mechanics and Durability Branch. Associate
Fellow AIAA
^Senior Staff scientist. Member AIAA
^Aerospace Engineer, Analytical & Computational
Methods Branch. Member AIAA
5 Aerospace Engineer, Mechanics and Durability
Branch. Member AIAA
'Copyright ©2001 by the American Institute of Aero-
nautics and Astronautics, Inc. No copyright is asserted
in the United States under Title 17, U.S code. The U.S
Government has a royalty-free license to exercise all rights
under the copyright claimed herein for Government Pur-
poses. All other rights are reserved by the copyright
owner.
The use of composite materials for aircraft
primary structures can result in significant ben-
efits on aircraft structural cost and performance.
Such applications of composites materials are ex-
pected to result in a 30-40 percent weight savings
and a 10-30 percent cost reduction compared to
conventional metallic structures. However, un-
like conventional metallic materials, composite
structures fail under different failure modes such
as matrix cracking, fiber-matrix shear failure,
fiber failure, and delamination. The initiation
of damage in a composite laminate occurs when
a single ply or part of the ply in the laminate fails
in any of these failure modes over a certain area
of the structure. The initiation of damage does
not mean that the structure cannot carry any
additional load. The residual load bearing capa-
bility of the composite structure from the onset
of material failure or initiation of damage to fi-
nal failure can be quite significant. It is at the
final failure load that the structure cannot carry
any further load. This may be due to the fact
that some failure modes may be benign not to
degrade the performance of the overall structure
significantly. Accurate determination of failure
modes and their progression helps either to de-
vise structural features for damage containment
or to define fail-safe criteria. Therefore it is im-
portant to understand the damage progression in
//v^.
.'f <.l
composite structures subjected to different load-
ing conditions.
Considerable work has been performed on
this subject. In 1987, Talreja ([1]), Allen et al.
([2]), and Chang and Chang ([3]), independently
proposed progressive failure models that describe
the accumulation of damage in a composite lam-
inate by a field of internal state variables. The
damage model proposed by Chang and Chang
([3]) for notched laminate loaded in tension ac-
counts for all of the possible failure modes ex-
cept delamination. Chang and Lessard ([4]) later
investigated the damage tolerance of composite
laminates subjected to compression. Davila et
al. ([5]) extended Chang and Lessard method
from two dimensional membrane effects to shell-
based analysis that includes bending. Shell-based
progressive failure analyses that apply a mate-
rial degradation model at every material point
in every ply in the laminate have been reported
in References [6] through [9]. Recently a shell-
based progressive failure analysis which consid-
ered large rotations based on a total Lagrangian
approach method was presented in Reference
[10].
The objective of the. present paper is to de-
velop and validate an efficient methodology that
can predict the ultimate strength of compos-
ite panels by taking into account ply damage
modes and geometrical non-linear response. Re-
sults from progressive failure analyses of compos-
ite panels with and without a cutout subjected to
shear and compressive loads are compared with
experimental results. In this paper progressive
failure results are compared with experimental
results for flat panels with and without cutout
subjected in-plane shear loading. Progressive
failure results are also presented for curved panels
with and without a cutout and subjected to ax-
ial compression. Although results from such ex-
perimental studies have been compared by other
authors with postbuckling cuialyses results, pro-
gressive failure analyses for nonlinearly deformed
structures is not reported in the open literature.
Thus another objective for this paper is to pro-
vide such a comparison.
Failure Analysis
Failure modes in laminated composite panels
are strongly dependent on ply orientation, load-
ing direction and panel geometry. There are four
basic modes of failure that occur in a laminated
composite structure. These failure modes are;
matrix cracking, fiber-matrix shear failure, fiber
failure, and delamination. Delamination failure,
however, is not included in the present studies. In
order to simulate damage growth accurately, the
failure analysis must be able to predict the fail-
ure mode in each ply and apply the corresponding
reduction in material stiffnesses. The failure cri-
teria included in the present analyses are those
proposed by Hashin [11] and are summarized be-
low.
• Matrix failure in tension and compression
occurs due to a combination of transverse,
iT22, and shear stress, T12, na and t-23- The
failure index can be defined in terms of
these stresses and the strength parame-
ters Y and shear allowables Sc- Failure
occurs when the index exceeds unity. As-
suming linear elastic response, the failure
index has the form:
e' =
-i-
CT22
Yc
and
„2 _
-I-
T12
Scl2
T23
•5c23
CT22
Yt
T23
Sc23
25c23
2
+
1
+
(72 2
25,
c23
Tl3
5cl3
for (T22 <
(1)
-I-
T12
'cl2
Tl3
'cl3
for 022 >
(2)
where Yt is the strength perpendicular to
the fiber direction in tension, Yc is the
strength perpendicular to the fiber direc-
tion in compression, and Scu, Sci3, and
5c23 are the in-plane shear, and transverse
shear strengths, respectively.
• Fiber-matrix shear failure occurs due to a
combination of axial stress (cru) and the
shear stresses. The failure criterion has
the form:
e' =
Ac/ \^cV2
2
(^) for an < (3)
\Jc\.3 J
and
el =
Scl2
+ (~) for an > (4)
\Ocl3/
where A'( is the strength along the fiber
direction in tension, and Xc is the strength
along the fiber direction in compression.
• Fiber failure occurs due to tension or com-
pression independent of the other stress
component. In compression the fiber fails
by buckling. The failure criterion has the
form:
6/ = -^ for an < (5)
and
e/ =
^11
Xt
for an >
(6)
To simulate the above failure modes, the
elastic properties are made to be linearly depen-
dent on three field variables, FVl through FV3.
The first field variable represents the matrix fail-
ure, the second the fiber-matrix shearing failure,
and the third the fiber buckling failure. The val-
ues of the field variables are set to zero in the
undamaged state. After a failure index has ex-
ceeded 1.0, the associated user-defined field vari-
able are set to 1.0. The associated field vari-
able then continues to have the value of 1.0, even
though the stresses may reduce to values lower
than the failure stresses of the material. This pro-
cedure ensures that the damaged material does
not heal. The mechanical properties in the dam-
aged area are reduced appropriately, according to
the property degradation model defined in Table
1. For example, when the matrix failure crite-
rion takes the value of 1.0, then by the interpola-
tion rule defined in Table 1, the transverse shear
modulus (Ey) cind the Poisson ratio (1/12) axe set
equal to zero. The field variables can be made to
transit from (undamaged) to 1 (fully damaged)
instantaneously. Chang and Lessard's degrada-
tion model [4] is used in the present study.
The finite element implementation of this
progressive failure analysis was developed for
the ABAQUS structural analysis program using
the USDFLD user-written subroutine [12, 13].
ABAQUS calls this USDFLD subroutine at all
material points of elements that have material
properties defined in terms of the field variables.
The subroutine provides access points to a num-
ber of variables such as stresses, strains, mate-
rial orientation, current load step, and material
name, all of which can be used to compute the
field variables. Stresses and strains are computed
at each incremental load step and evaluated by
the failure criteria to determine the occurrence of
failure and the mode of failure.
Numerical Examples
To assess the predictive capability of the
present failure analysis method, several panels
have been analyzed and these results were com-
pared with experimental results. Results are pre-
sented for unstiffened panels with and without
cutouts and a stiffened panel. The unstiffened
panel cases are a flat panel loaded in shear and
a curved panel loaded in compression. Results
are also presented for a bead-stiffened panel sub-
jected to in-plane shear loading.
Flat Panel Loaded in In-plane Shear
The panels subjected to pure in-plane shear
loading were loaded using a picture frame fix-
ture. The test sections of the bead-stiffened and
unstiffened panel were 12.0 by 12.0 in. in size
and the members of the picture frame were 2.75-
in. wide and 6.75-in thick. The fixture is made
of steel. Figure 1 shows a schematic diagram of
a picture frame test fixture. In the finite ele-
ment model, nodes on each member were con-
strained for the out-of-plane displacement. Pin
joint consists of two co-incident nodes tied in
a multi-point constraint at the four corners of
the panel. The displacements of the dependent
node is made the same as that of the indepen-
dent node, but the rotations of the co-incident
nodes are excluded in the multi-point constraints.
The independent node diagonally opposite to the
loading pin is constrained for axial and transverse
displacements. At the loading pin, applied dis-
placement equal in magnitude in the axial and
transverse directions at the independent node
simulates the loading condition. The test section
is modeled using ABAQUS four node, reduced
integration, shear deformable S4R element [13].
The members of the picture frame are modeled
using ABAQUS four node shear deformable S4
element [13].
The flat unstiffened panel has a lami-
nate stacking sequence of [±4o/0/90]2s, with
a ply thickness of 0.0056-in. and is made
of graphite epoxy. The mechanical properties
for the material are £u = 18.5 Msi, £22 = 1-64
Msi, Gi2=Gi3=0.87 Msi, G23=0.55 Msi, and
1/12=0.3. The strength allowables are A't=232.75
ksi, A'e=210.0 ksi, V; = 14.7 ksi, re=28.7 ksi,
Sc:i2=29.75 Ksi, and 5ci3=5c23=4.8 ksi. Experi-
mental results for this test panel are reported in
Reference [14].
A finite element model of the panel is shown
in Figure 2. This model consists of 3425 nodes
and 3300 elements. An imperfection based on
static analysis results for a pressure load was
added to the model to simulate an imperfect
shape similar to that of a bubble (one half wave
in each direction of the panel). Progressive fail-
ure analysis (PFA) was carried out for this case
with a mciximum imperfection magnitude equal
to 5% of the laminate thickness. Three integra-
tion points through each ply thickness are used
in the analysis for computation of section prop-
erties. A post-buckling analysis of the panel
with the same level of imperfection was also per-
formed.
The results for the flat pcuiel loaded in shear
are shown in Figure 3, where the load is plotted
versus the strain normal to the fiber direction
(£22) in the top and bottom ply (45° ply) at the
center of the test specimen. The dashed lines
marked FVl, FV2 and FV3 indicate the load
level at which damage described by field vari-
able FVl through FV3 are initiated well into
the post buckling regime. These failures are due
to severe bending in the region. The thick solid
line represents the experimental results and the
thin solid line represents the postbuckling analy-
sis results. The solid and open triangles are an-
alytical results for the panel response that indi-
cates progression of failure. The analysis results
are in good agreement with the experimental re-
sults. The final failure load obtained from the
experiment is 54.81 kips, which is 6 % more than
the final failure load of approximately 51.5 kips
obtained from progressive failure analysis. Dam-
age initiation starts as matrix cracking (FVl) at
a load level of 37.76 kips. Fiber-matrix shear
{FV2), and fiber (F73) failure are initiated at
the same load level of 45.37 kips. This indicates
that the structure can carry an additional 17.04
kips (about 30% of the final experimental load)
after matrix cracking has been initiated. Even af-
ter the initiation of fiber-matrix shear and fiber
failure, the panel continues to carry an additional
load of about 9.4 kips ( 17% of the final experi-
mental load). The post-buckling analysis results
diverge from the progressive failure results at a
load level that is slightly higher than the load at
which initiation of fiber-matrix shear and fiber
failure occurs. At that load level the analysis pre-
dicts a significant amount of damage that could
have led to a considerable loss of panel stiff'ness.
All the failure modes initiated near the steel
supporting fixture close to the region along the
diagonal which is in the panel loading direction
and propagate in the region close to the diagonal
and along the loading direction. Figure 4 shows
a fringe plot of matrix cracking (FVl) in the top
ply after the final failure load. The dark contours
denote failed regions of the panel. Other damage
modes accumulate in approximately the same re-
gion as depicted by the plot. These damage loca-
tions are consistent with observations from exper-
iments and do not involve delamination failure.
Curved Panel Loaded in Axial Compression
The curved panel has a laminate stacking
sequence of [±45/0/90]3s, with a ply thickness
of 0.005-in. The mechanical properties of the
material used for the panel are £ii = 17.5 Msi,
£22=1-51 Msi, Gi2=Gi3=0.78 Msi, ^23=0.55
Msi, and 1^12=0.29. The strength allowables £u:e
Xt=206.0 ksi, Xc=206.0 ksi, Yt=8.9 ksi, Yc=17.8
ksi, 5ci2 = 18.3 Ksi, and 5ci3=Sc23=4.8 ksi. Ex-
perimental results for this test are reported in
Reference [15].
The panel geometry, boundary conditions
and loading are shown in Figure 5. The panel
finite element model consists of 6561 nodes and
6400 elements. Measured geometric imperfection
from a typical test specimen was included in the
model. Three integration points through each ply
thickness are used in the analysis for computation
of section properties.
The results for the curved panel loaded in
compression are shown in Figure 6, where the
load is plotted against the end shortening dis-
placement. The filled symbols representing FVl,
FV2, and FV3 indicate the load level at which
damage described by field variable FVl through
FV3 are initiated. The analysis and expermental
results are in good agreement. The final failure
load from the experiment is 51.25 kips, which is
1 1 % less than the final failure load obtained from
progressive failure analysis of about 56.8 kips. All
damage modes initiate after the panel buckling
and attaining its final load bearing capability.
Matrix cracking {FVl) initiated at a load level
of 43.31 kips just after buckling. Fiber-matrix
shear (FV'2) and fiber failure (FV'3) initiated at
a load level of 37.53 kips and a load level of 38.32
kips, respectively.
Figure 7(a) through 7(c) show fringe plots
for matrix cracking (FVl), fiber matrix shear
(FV2), and fiber failure (FV3) in the bottom ply
after final failure at an applied displacement of
approximately 0.1-in.. Damage initiated within
than the experimental failure load. Damage initi-
ation starts as fiber-matrix shear {FV2) and fiber
(FV3) failure at the same load level of 28.34 kips.
Matrix cracking {FVl) is initiated at a load level
of 30.22 kips. Hence the curved panel can carry
an additional load of about 11.0 kips (about 27%
of the final experimental load) after initiation of
fiber-matrix shear and fiber failure. After matrix
cracking heis been initiated, the panel can carry
an additional load of 9.0 kips (about 23% of the
final experimental load).
All the failure modes initiated near the edge
of the cutout. Figure 12 shows a fringe plot for
matrix cracking (FVl) in the bottom ply after
the final failure load. These damage locations are
consistent with experimental observations. How-
ever experimental observation indicated signifi-
cant delamination around the cutout. Although
the initial geometric imperfection are accurately
represented here, the delamination damage may
be responsible for the discrepancy between the
analytical and experimental failure loads with the
panel exhibiting a catastrophic failure with no
residual strength.
Bead-stiffened Panel Loaded in Shear
The thermoformed bead- stiffened configura-
tion is an advanced concept for stiffened graphite
thermoplastic panels. Thermoforming ia a cost
effective manufacturing method for incorporat-
ing bead stiffeners. An experimental and analyt-
ical investigation of these bead-stiffened panels
was conducted by Rouse [17]. The bead-stiffened
panels were loaded in in-plane shear loading us-
ing a picture frame fixture similar to the one de-
scribed above. It was found that the bead stiflF-
ened panels failed near the curved tip of the stiff-
ener where large magnitudes of stress resultants
were predicted.
The bead-stiffened panel has a laminate
stacking sequence of [±45/ ± 45/0/ ± 45/90]s
with a ply thickness of 0.005-in. The mechan-
ical properties of the material are £^u = 18.0
Msi, £22=1.50 Msi, Gi2=Gi3=G23=0.82 Msi.
The allowables are X(=300.0 ksi, Xc=210.0 ksi,
Yt=l3.0 ksi, n=31.0 ksi, Sci2=27.0 Ksi, and
5ci3=Sc23=5.0 ksi. A finite element model of
the bead-stiflened panel is shown in Figure 13.
This model consists of 2935 nodes and 2849 ele-
ments. No geometric imperfection was added to
the model of the bead-stiffened panel. Three in-
tegration points through each ply thickness are
used in the analysis for computation of section
properties.
The results for this in-plane shear-loaded
panel are shown in Figure 14, where the load is
plotted versus the axial strain {e^^x) in the top
and bottom plies (45° ply) at the center of the
test panel. The curves FVl, FV2, and FV3 in-
dicate the load level at which damage modes de-
scribed by the field variable FVl through FV3
initiate. The analyses results sire in good agree-
ment with the experimental results. The final
failure load obtained from the experiment is 27.9
kips, which is 12 % less than the final failure load
obtained from the progressive failure analysis of
about 24.4 kips. Damage initiation starts as ma-
trix cracking (FVl) at a load level of 10.8 kips,
whereas fiber-matrix shear {FV2) and fiber fail-
ure are initiated at the same load level of 12.8
kips. Hence the structure can carry an additional
load of approximately 17.0 kips (60% of the final
experimental load) after matrix cracking damage
has been initiated. Even after initiation of fiber-
matrix shear and fiber failure, the panel can carry
an additional load of approximately 15.0 kips (
53% of the final experimental load).
Figure 15(a) through 15(c) show fringe plots
for matrix cracking, fiber-matrix shear, and fiber
failure in the top ply after the final failure load.
The damage initiated near the curved tip of the
bead-stiflener and propagated to the other re-
gions as shown in these figures. The locations
for damage are consistent with experimental ob-
servations. For the case of this stiffened panel,
initial geometric imperfections are not a criticeJ
factor in predicting the observed behavior.
Concluding Remarks
The results of an analytical and experimen-
tal study to evaluate the initiation and progres-
sion of damage in nonlinearly deformed stiffened
sdid unstiffened panel are presented. These stud-
ies are also conducted for panels with cutouts
and subjected to two loading conditions. The
progressive failure methodology includes matrix
cracking, fiber-matrix shear, and fiber failure,
but ignores delamination failure. The effect of
initial geometric imperfections is also investi-
gated as part of the study.
For a flat panel loaded in in-plane shear load-
ing, the three failure modes considered in the
study accurately represent the damage senario in
the postbuckling regime. The analytically deter-
mined response, failure modes and damage loca-
tions compare well with the experimental results
when the initial geometric imperfection is in-
cluded in the analysis in a simple manner. When
6
/■' >- ^,
a cutout is introduced, however, delamination oc-
curs at the hole boundary as an additional fail-
ure mode resulting in some discrepancies with the
observed behavior. The analysis results also pre-
dict a residual strength with the final failure load
being approximately 10% greater than the exper-
imental failure load.
The response of curved panels with and
without cutouts are studied when loaded in com-
pression. With measured geometric imperfection
included in both curved panel models, the re-
sponse of the panel without cutout compares well
with experimental results. No delamination oc-
curs for this case and the failure modes consid-
ered in this paper develop after buckling. For
the curved panel with a cutout, however delam-
ination does occur with the panel failing catas-
trophically. Unlike the panel without a cutout,
this panel with a cutout exhibits no residual
strength. It may be important to include de-
lamination failure mode to predict the residual
strength of curved panels with a cutout of the
type considered here.
The bead-stiffened panel response, failure
modes and damage locations are well predicted
by the analysis results. The residual strength val-
ues from the analysis and experiment are within
12 percent with no geometric imperfection in-
cluded in the analysis.
References
[1] Talreja, R., "Modeling of Damage Develop-
ment in Composites using Internal Variable
Concepts," Damage Mechanics in Compos-
ites, AD Vol. 12, Proceedings of the ASMS
Winter Annual Meeting, Boston, MA, 1987,
pp. 11-16.
[2] Allen, D. H., Harris, C, and Groves, S.
E., "A Thermomechanical constitutive The-
ory for Elastic Composites with Distributed
Damage, Part I. Theoretical Development,"
International Journal of Solids and Struc-
tures, Vol. 23, No. 9, 1987, pp. 1301-1318.
[3] Chang, F.-K., and Chang, K. Y., "A Pro-
gressive Damage Model for Laminated Com-
posites Containing Stress Concentrations,"
Journal of Composite Materials, Vol. 21,
Sept. 1987, pp. 834-855.
[4] Chang, F.-K., and Lesard, L. B., "Damage
Tolerance of Laminated Composites Con-
taining an Open Hole and Subjected to
Compressive Loadings: Part 1-Analysis,"
Journal of Composite Materials, Vol. 25,
Jan. 1991, pp. 2-43.
[5] Davila, C. G., Ambur, D. R., and Mc-
Gowan, D. M., "Analytical Prediction of
Damage Growth in Notched Composite Pan-
els Loaded in Compression," Journal of Air-
craft, Vol. 37, No. 5, pp. 898-905.
[6] Minnetyan, L., Chamis, C. C, and Murthy,
P. L., "Damage and Fracture in Compos-
ite Thin Shells," NASA TM-105289, Nov.,
1991.
[7] Averill, R. C, "A Micromechanics-Based
Progressive Failure Model for Laminated
Composite Structures," Proceedings of
the 33rd AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics, and Mate-
rials Conference, AIAA, Washington, DC,
1992, pp. 2898-2904.
[8] Moas, E., "Progressive Failure Analysis of
Laminated Composite Structures," Ph.D
Dissertation, Engineering Mechanics Dept.,
Virginia Polytechnic Inst, and State Univ.,
Blackburg, VA 1996.
[9] Sleight, D. W., Knight, N. F. Jr., and
Wang, J. T., "Evaluation of a Progres-
sive Failure Analysis Methodology for Lam-
inated Composite Structures," Proceedings
of the 38th AIAA/ASME/ASCE/AHS/ASC
Structures, Structural Dynamics, and Ma-
terials Conference, Reston, VA, 1997, pp.
2257-2272.
[10] Gummadi, L. N. B., and Palazotto, A. N.,
"Progressive failure Analysis of Composite
Shells considering Large Rotations," Com-
posite Part B, Vol. 29, 1998, pp. 547-563.
[11] Hashin, Z., "Failure Criteria for Unidirec-
tional Fiber Composites," Journal of Ap-
plied Mechanics, Vol. 47, June 1980, pp. 329-
334.
[12] ABAQUS User's Manual, Vol. 3, Ver. 5.6,
Hibbitt, Karlsson, and Sorensen, Pawtucket,
RI, 1996, pp. 25.2.33-1.
[13] ABAQUS Example Problems Manual, Vol.
1, Ver. 5.5, Hibbitt, Karlsson, and Sorensen,
Pawtucket, RI, 1995, pp. 3.2.25.25-1.
[14] Rouse, M., "Post Buckling of Flat
UnstifFened Graphite-Epoxy Plates
Loaded in Shear," Presented at the
AIAA/ASME/ASCE/AHS 26th Structures,
Structural Dynamics, and Materials Confer-
ence, Orlando, Florida, April 15-17, 1985.
Also AIAA Paper No. 85-0771-CP.
[15] Hiburger, M. W., Britt, V. 0., and
Nemeth, M. P., "Buckling Behavior of
Compression-loaded Quasi-isotropic Curved
Panel with a Circular Cutout," 40th
AIAA/ASME/ASCE/AHS/ASC Struc-
tures, Structural Dynamics and Materials
Conference, St. Louis, MO , Paper AIAA-
99-1279, April 12-15, 1999.
[16] Rouse, M., "Effect of Cutouts or Low-speed
Impact Damage on the Postbuckling Behav-
ior of Composite Plates Loaded in Shear,"
Presented at the AIAA/ASME/ASCE/AHS
31th Structures, Structural Dynamics, and
Materials Conference, Long Beach, Califor-
nia, April 2-4, 1990. Also AIAA Paper No.
90-0966-CP.
[17] Rouse, M., "Structural Response of Bead-
stiffened Thermoplastic Shear Webs," First
NASA Advanced Composite Technology
Conference, Oct. 29-Nov. 1, 1990., NASA
Conference Publication 3104, pp. 969-977.
Table 1: Dependence of material elastic
properties on the field variables
No Matrix
failure cracking
Fiber-matrix,
shear
Fiber
failure
En
En
En
En ->0
£/22
E22
->0
■^22
£^22 ^0
1^12
V12
-^0
1^12 ->o
1/12 ^0
Gi2
Gn
G12 ^0
Gi2^0
G,3
Gl3
Gi3 ->0
Gi3 -^0
G23
G23
G23
G23 ^0
FV'1=0
FV'1 = 1
FV'1=0
FV'1=0
fV'2=0
FV'2=0
FV2=l
FV'2=0
FV2=0
FV'3=0
FV'3=0
FV3^l
frame member
\Z
Loading
direction
1
^
45 deg.
test
section
frame
member
• Pin joint
Figure 1 Schematic diagram of picture frame
test fixture.
Figure 2 Finite element model of a flat
composite panel in the picture frame test
fixture.
Post-buckling
analyses
10000
-8.02-0.015-0.01 -O.OOS 0.005 0.01 0.01 S 0.1
strain (Ejj), inVin.
Figure 3 Load vs. strain component normal to
fiber direction in top and bottom plies of flat
panel loaded in the picture frame test fixture.
0.05
End-shortening, in.
Figure 6 Load vs. end-shortening displacement
results for curved panel loaded in compression.
Figure 4 Fringe plot for matrix cracking {FVl)
in the top ply of the flat pcinel.
Figure 7(a) Fringe plot for matrix cracking in
the bottom ply for curved panel loaded in
compression.
Figure 7(b) Frmge plot for fiber-matrix shear in
Figure 5 Geometry and boundary conditions for the bottom ply for curved panel loaded in
curved composite panel. compression.
■ iff Mil ^ ^ J.* ' '^ 1* •IV'
Figure 7(c) Fringe plot for fiber failure in the
bottom ply for curved panel loaded in
compression.
Figure 10 Fringe plot for fiber failure in the top
ply for the flat panel with a cutout loaded in
the picture frame test fixture.
Failure
Figure 8 Finite element model of flat panel with
a circular cutout.
0.02 0.04 0.06
End-shortening, In.
0.12
0,# Experiment
A, A 1%t Imperfection
D,l 5%t Impeilectlon
Figure 11 Load versus end-shortening
displacement for a curved panel with cutout
{d/W=0.2) and subjected to axial compression
loading.
Figure 9 Load vs. strain component normal to
fiber direction in the top and bottom plies of
flat panel with a cutout loaded in the picture
frame test fixture.
Figure 12: Plot for matrix cracking damage in
the bottom ply for curved panel with cutout
{d/W-Q.2) and loaded in compression.
10
Figure 13: Finite element model of the
bead-stiffened panel in picture frame test
fixture.
Figure 15(b) Fringe plot for fiber-matrix shear
in the top ply of the bead-stiffened panel
top ply
0}PFA
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Strain (E„)
Figure 14: Load versus axial strain, (en) results
at the center of bead-stiffened panel.
Figure 15(c) Fringe plot for fiber failure in the
top ply of the bead-stiffened panel
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Figure 15(a) Fringe plot for matrix cracking in
the top ply of the bead-stiffened panel
11
July 26, 2001
NASA STI Acquisitions DAA Authorization
The following papers (copies enclosed) have been DAA approved as Unclassified, Publicly Avail-
able documents:
Meeting Presentations: nm c \>j\
42nd AIAA/ASME/ASCE/AHS Structures, Structural Dyn..., 4/16-19/2001, Seattle, WA:
TF Johnson et al ■ High Temperature Polyimide Materials in Extreme Temperature...
D A Russell,' er al.: Effects of Electrons, Proton, and Ultraviolet Radiation on Thermo...
J Arbocz et al ■ On the Accuracy of Probabilistic Buckling Load Predictions.
j' Arbocz! et al.: On a High-Fidelity Hierarchical Approach to Buckling Load Calculations.
M P Nemeth: Buckling Behavior of Long Anisotropic Plates Subjected to Fully
D R Ambur et al : Progressive Failure Studies of Composite Panels With and Without...
M W. Hilburger, et al.: High-Fidelity Nonlinear Analysis of Compression-Loaded...
M W Hilburger, et al.: Nonlinear Analysis and Scaling Laws for Noncircular Composite
M w' Hilburger, et al.: NonUnear and Buckling of Curved Panels Subjected to Combined...
J C Newman, et al. : A Review of the CTOA/CTOD Fracture Criterion - Why it Works
10th AlAA/NAL-NASDA-ISAS Int'l Space Plane & Hypersonic..., 4/24-27/2001, Kyoto, Japan:
C R McClinton, et al.: Hyper-X Program Status.
American Helicopter Society 57th Annual Forum, 5/9-1 1/2001, Washington, DC:
M L Wi^ur .r al ■ Vibmtoiy Loads Reduction Testing of the NASA/ARMY/MIT Active...
7th AlAA/CEAS Aeroacousiics Conference, 5/28-30/2001, Maastricht, The Netherlands:
L Maestrello: Laminarization of Turbulent Boundary Layer on Flexible and Rigid Structures.
15th AlAA Computational Fluid Dynamics, 6/11-14/2001, Anaheim, CA:
D. Sidilkover, et al.: Factorizable Upwind Schemes: The Triangular Unstructured Grid...
Susan H. Stewart
^» . r. . ,■ ,^ s.h.stewart@larc.nasa.gov
DAA Representative ^- n^n\9.(^ l^\9,
Hampton, VA 23681-2199